In a binary max heap containing n numbers, the smallest element can be found in time

Which one of the following grammars generates the following language?

$$L = \left( {{a^i}{b^j}|i \ne j} \right)$$

Consider the following grammar.

$$\eqalign{ & S \to S*E \cr & S \to E \cr & E \to F + E \cr & E \to F \cr & F \to id \cr} $$

Consider the following LR(0) items corresponding to the grammar above.

$$\eqalign{ & (i)\,S \to S*.E \cr & (ii)\,E \to F. + E \cr & (iii)\,E \to F + .E \cr} $$

Given the items above, which two of them will appear in the same set in the canonical sets-of-items for the grammar?

In the correct grammar of the previous question, what is the length of the derivation (number of steps starring from S) to generate the string $${a^l}{b^m}$$ with $$l \ne m$$?